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arXiv · 1402.3159

Ramanujan type congruences for the Klingen-Eisenstein series

Toshiyuki Kikuta·Sho Takemori
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Abstract

In the case of Siegel modular forms of degree $n$, we prove that, for almost all prime ideals $\frak{p}$ in any ring of algebraic integers, mod $\frak{p}^m$ cusp forms are congruent to true cusp forms of the same weight. As an application of this property, we give congruences for the Klingen-Eisenstein series and cusp forms, which can be regarded as a generalization of Ramanujan's congruence. We will conclude by giving numerical examples.

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BibTeXRIS

Toshiyuki Kikuta, Sho Takemori. 2014-02-13. Ramanujan type congruences for the Klingen-Eisenstein series. https://arxiv.org/abs/1402.3159

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